Question

Please help answer questions (a)-(c).

Objective 4: Use the Empirical Rule to Describe Data That Are Bell-Shaped 3.2 Measures of Dispersion 3.2.29 0 of 1 Point Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 11. Use the empirical rule to determine thefollowing (a) What percentage of people has an IQ score between 67 and 133? (b) What percentage of people has an IQ score less than 67 or greater than 1333 (c) What percentage of people has an IQ score greater than 122? (a)% (Type an integer or a decimal.)

Answer 1

Solution:-

Mean = 100, S.D = 11

a) The percentage of people has an IQ score between 67 and 133 is 99.7%.

x₁ = 67

x₂ = 133

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

z₁ = -3

z₂ = 3

P( -3.0 < z < 3.0) = 0.997

P( -3.0 < z < 3.0) = 99.7%

b) The percentage of people has an IQ score less than 67 and or greater than 133 is 0.3%.

x₁ = 67

x₂ = 133

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

z₁ = -3

z₂ = 3

P( -3.0 > z > 3.0) = 1 - 0.997

P( -3.0 > z > 3.0) = 0.003

P( -3.0 > z > 3.0) = 0.3%

c) The percentage of people has an IQ score greater than 122 is 2.5%.

x = 122

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

z = 2

P(z > 2) = (1 - 0.95)/2

P(z > 2) = 0.025

P(z > 2) = 2.5%